How do I radial gradient shade an open object?
A simple gradient texture would do this. Use a gradient texture (I used spherical) with object texture coordinates (add the object you want the coordinates to come from in the Texture Coordinate node), and a *Color Ramp (Ease interpolation* would probably give the best result) to adjust the contrast as a mask between two shaders as shown below:

Click to enlarge
Also, it is important to apply scale to see correct results.

This should give you a result like this:

Here is the modified file: